Hypercharge
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In
particle physics Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
, the hypercharge (a portmanteau of hyperonic and
charge Charge or charged may refer to: Arts, entertainment, and media Films * '' Charge, Zero Emissions/Maximum Speed'', a 2011 documentary Music * ''Charge'' (David Ford album) * ''Charge'' (Machel Montano album) * ''Charge!!'', an album by The Aqu ...
) ''Y'' of a
particle In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object which can be described by several physical property, physical or chemical property, chemical ...
is a
quantum number In quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can be kno ...
conserved under the
strong interaction The strong interaction or strong force is a fundamental interaction that confines quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is called the n ...
. The concept of hypercharge provides a single charge operator that accounts for properties of
isospin In nuclear physics and particle physics, isospin (''I'') is a quantum number related to the up- and down quark content of the particle. More specifically, isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions ...
,
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
, and flavour. The hypercharge is useful to classify
hadron In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite subatomic particle made of two or more quarks held together by the strong interaction. They are analogous to molecules that are held together by the ele ...
s; the similarly named
weak hypercharge In the Standard Model of electroweak interactions of particle physics, the weak hypercharge is a quantum number relating the electric charge and the third component of weak isospin. It is frequently denoted Y_\mathsf and corresponds to the gauge ...
has an analogous role in the
electroweak interaction In particle physics, the electroweak interaction or electroweak force is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very differe ...
.


Definition

Hypercharge is one of two
quantum number In quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can be kno ...
s of the SU(3) model of hadrons, alongside
isospin In nuclear physics and particle physics, isospin (''I'') is a quantum number related to the up- and down quark content of the particle. More specifically, isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions ...
 . The isospin alone was sufficient for two
quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All commonly o ...
flavours — namely and — whereas presently 6  flavours of quarks are known. SU(3) weight diagrams (see below) are 2 dimensional, with the coordinates referring to two quantum numbers: (also known as ), which is the  component of isospin, and , which is the hypercharge (the sum of
strangeness In particle physics, strangeness ("''S''") is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic interactions which occur in a short period of time. The strangeness of a parti ...
 ,
charm Charm may refer to: Social science * Charisma, a person or thing's pronounced ability to attract others * Superficial charm, flattery, telling people what they want to hear Science and technology * Charm quark, a type of elementary particle * Ch ...
 ,
bottomness In physics, bottomness (symbol ''B''′ using a prime as plain ''B'' is used already for baryon number) or beauty is a flavour quantum number reflecting the difference between the number of bottom antiquarks (''n'') and the number of botto ...
 ,
topness Topness (''T'', also called truth), a flavour quantum number, represents the difference between the number of top quarks (t) and number of top antiquarks () that are present in a particle: :T = n_\text - n_\bar By convention, top quarks have a ...
 , and
baryon number In particle physics, the baryon number is a strictly conserved additive quantum number of a system. It is defined as ::B = \frac\left(n_\text - n_\bar\right), where ''n''q is the number of quarks, and ''n'' is the number of antiquarks. Bary ...
 ). Mathematically, hypercharge is :Y = B + S + C + B' + T' ~. Strong interactions conserve hypercharge (and
weak hypercharge In the Standard Model of electroweak interactions of particle physics, the weak hypercharge is a quantum number relating the electric charge and the third component of weak isospin. It is frequently denoted Y_\mathsf and corresponds to the gauge ...
), but
weak interaction In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction, ...
s do ''not''.


Relation with electric charge and isospin

The
Gell-Mann–Nishijima formula The Gell-Mann–Nishijima formula (sometimes known as the NNG formula) relates the baryon number ''B'', the strangeness ''S'', the isospin ''I3'' of quarks and hadrons to the electric charge ''Q''. It was originally given by Kazuhiko Nishijima and ...
relates isospin and
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
: Q = I_3 + \tfracY, where ''I''3 is the third component of isospin and ''Q'' is the particle's charge. Isospin creates multiplets of particles whose average charge is related to the hypercharge by: : Y = 2 \bar Q. since the hypercharge is the same for all members of a multiplet, and the average of the ''I''3 values is 0.


SU(3) model in relation to hypercharge

The SU(2) model has
multiplet In physics and particularly in particle physics, a multiplet is the state space for 'internal' degrees of freedom of a particle, that is, degrees of freedom associated to a particle itself, as opposed to 'external' degrees of freedom such as the ...
s characterized by a quantum number ''J'', which is the total
angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
. Each multiplet consists of substates with equally-spaced values of ''Jz'', forming a
symmetric Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...
arrangement seen in
atomic spectra Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wa ...
and isospin. This formalizes the observation that certain strong baryon decays were not observed, leading to the prediction of the mass, strangeness and charge of the baryon. The SU(3) has ''supermultiplets'' containing SU(2) multiplets. SU(3) now needs two numbers to specify all its sub-states which are denoted by ''λ''1 and ''λ''2. specifies the number of points in the topmost side of the
hexagon In geometry, a hexagon (from Ancient Greek, Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple polygon, simple (non-self-intersecting) hexagon is 720°. Regular hexa ...
while specifies the number of points on the bottom side.


Examples

* The
nucleon In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number (nucleon number). Until the 1960s, nucleons were ...
group (
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
s with and
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons beh ...
s with ) have an average charge of , so they both have hypercharge (since baryon number and ). From the Gell-Mann–Nishijima formula we know that proton has isospin while neutron has * This also works for
quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All commonly o ...
s: For the ''up'' quark, with a charge of , and an of , we deduce a hypercharge of , due to its baryon number (since three quarks make a baryon, each quark has a baryon number of ). * For a ''strange'' quark, with electric charge , a baryon number of , and
strangeness In particle physics, strangeness ("''S''") is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic interactions which occur in a short period of time. The strangeness of a parti ...
−1, we get a hypercharge so we deduce that That means that a ''strange'' quark makes an isospin singlet of its own (the same happens with ''charm'', ''bottom'' and ''top'' quarks), while ''up'' and ''down'' constitute an isospin doublet.


Practical obsolescence

Hypercharge was a concept developed in the 1960s, to organize groups of particles in the ''"
particle zoo In particle physics, the term particle zoo is used colloquially to describe the relatively extensive list of known subatomic particles by comparison to the variety of species in a zoo. In the history of particle physics, the topic of particles wa ...
"'' and to develop ''ad hoc'' conservation laws based on their observed transformations. With the advent of the
quark model In particle physics, the quark model is a classification scheme for hadrons in terms of their valence quarks—the quarks and antiquarks which give rise to the quantum numbers of the hadrons. The quark model underlies "flavor SU(3)", or the E ...
, it is now obvious that strong hypercharge, , is the following combination of the numbers of up (), down (),
strange Strange may refer to: Fiction * Strange (comic book), a comic book limited series by Marvel Comics * Strange (Marvel Comics), one of a pair of Marvel Comics characters known as The Strangers * Adam Strange, a DC Comics superhero * The title char ...
 (),
charm Charm may refer to: Social science * Charisma, a person or thing's pronounced ability to attract others * Superficial charm, flattery, telling people what they want to hear Science and technology * Charm quark, a type of elementary particle * Ch ...
 (),
top A spinning top, or simply a top, is a toy with a squat body and a sharp point at the bottom, designed to be spun on its vertical axis, balancing on the tip due to the gyroscopic effect. Once set in motion, a top will usually wobble for a few ...
 () and
bottom Bottom may refer to: Anatomy and sex * Bottom (BDSM), the partner in a BDSM who takes the passive, receiving, or obedient role, to that of the top or dominant * Bottom (sex), a term used by gay couples and BDSM * Buttocks or bottom, part of th ...
 (): : Y = \tfrac n_\textrm + \tfrac n_\textrm - \tfrac n_\textrm + \tfrac n_\textrm - \tfrac n_\textrm + \tfrac n_\textrm ~. In modern descriptions of
hadron In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite subatomic particle made of two or more quarks held together by the strong interaction. They are analogous to molecules that are held together by the ele ...
interaction, it has become more obvious to draw
Feynman diagram In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduc ...
s that trace through the individual constituent quarks (which are conserved) composing the interacting
baryon In particle physics, a baryon is a type of composite subatomic particle which contains an odd number of valence quarks (at least 3). Baryons belong to the hadron family of particles; hadrons are composed of quarks. Baryons are also classified ...
s and
meson In particle physics, a meson ( or ) is a type of hadronic subatomic particle composed of an equal number of quarks and antiquarks, usually one of each, bound together by the strong interaction. Because mesons are composed of quark subparticles ...
s, rather than bothering to count strong hypercharge quantum numbers. ''
Weak hypercharge In the Standard Model of electroweak interactions of particle physics, the weak hypercharge is a quantum number relating the electric charge and the third component of weak isospin. It is frequently denoted Y_\mathsf and corresponds to the gauge ...
'', however, remains an essential part of understanding the
electroweak interaction In particle physics, the electroweak interaction or electroweak force is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very differe ...
.


References

*{{cite book , first1=Henry , last1=Semat , first2=John R. , last2=Albright , title=Introduction to Atomic and Nuclear Physics , publisher=Chapman and Hall , year=1984 , isbn=978-0-412-15670-0 Nuclear physics Quarks Standard Model Electroweak theory he:היפרמטען